Figure 1 should bring to mind the graph (see fig. 2)Image courtesy of C. Lygouras, “Critical behavior of the order parameter and specific heat in the second-order phase transition from Landau theory", May 4, 2020. Wikimedia Commons contributors, `File:LandauTheoryTransitions.svg`, Wikimedia Commons, the free media repository. of the order parameter as a function of temperature in the Ginzburg-Landau (GL) mean-field theory of second-order phase transitions where the order parameter is zero above a critical temperature \(T_c\)  but increases above zero below \(T_c\) . Our critical coupling \(\xi _c\)  is the analog to the critical temperature \(T_c\) . We can make this connection more quantitative. In GL mean-field theory, at temperatures \(T\)  below and near \(T_c\) , the order parameter is proportional to \((T_c-T)^{1/2}\,\)[1]}, [2]} a power law behaviour with critical exponent of \(1/2\) . The VEV for \(\xi \)  below and near \(\xi _c\)  has a similar behaviour. Using (REF ), we can express \(\Lambda \)  in terms of \(\xi _c\)  and substitute this into (REF ) to obtain
\(v_{eff}=\Bigg [\,2 v^2+\frac{\alpha }{\xi }-\frac{\sqrt{\alpha ^2+2 \,v^2\, \alpha \,\xi + v^4 \,\xi ^2-\frac{\xi ^2 \,\left(-2 \,v^2 \,\alpha \,\lambda -3 \,v^4 \,\lambda \,\xi _c\right)}{\lambda \,\xi _c}}}{\xi }\,\Bigg ]^{1/2}\,.\) 
